Base field 5.5.195829.1
Generator \(w\), with minimal polynomial \(x^{5} - 2x^{4} - 5x^{3} + 6x^{2} + 7x + 1\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2, 2]$ |
| Level: | $[16, 16, -w^{4} + 2w^{3} + 5w^{2} - 7w - 7]$ |
| Dimension: | $4$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $15$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{4} + 6x^{3} - 5x^{2} - 28x + 28\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, -w^{2} + 2w + 1]$ | $\phantom{-}0$ |
| 11 | $[11, 11, -w^{4} + 2w^{3} + 4w^{2} - 6w - 2]$ | $-\frac{1}{2}e^{3} - 4e^{2} - \frac{7}{2}e + 11$ |
| 13 | $[13, 13, -w^{4} + 3w^{3} + 3w^{2} - 9w - 3]$ | $\phantom{-}e$ |
| 13 | $[13, 13, -w^{2} + w + 3]$ | $\phantom{-}e^{3} + 7e^{2} + 3e - 20$ |
| 16 | $[16, 2, w^{4} - 3w^{3} - 4w^{2} + 10w + 5]$ | $-\frac{1}{2}e^{3} - 3e^{2} - \frac{1}{2}e + 6$ |
| 17 | $[17, 17, -w^{4} + 2w^{3} + 5w^{2} - 6w - 5]$ | $\phantom{-}e^{3} + 7e^{2} + 3e - 22$ |
| 23 | $[23, 23, -w^{2} + 2]$ | $-\frac{1}{2}e^{3} - 4e^{2} - \frac{7}{2}e + 11$ |
| 29 | $[29, 29, w^{4} - 2w^{3} - 5w^{2} + 7w + 4]$ | $-\frac{1}{2}e^{3} - 3e^{2} + \frac{1}{2}e + 11$ |
| 31 | $[31, 31, w^{4} - 3w^{3} - 3w^{2} + 8w + 4]$ | $-2e - 6$ |
| 31 | $[31, 31, -w^{4} + 2w^{3} + 3w^{2} - 5w]$ | $-2e - 2$ |
| 37 | $[37, 37, 3w^{4} - 6w^{3} - 13w^{2} + 17w + 12]$ | $\phantom{-}e^{3} + 8e^{2} + 6e - 26$ |
| 59 | $[59, 59, w^{4} - w^{3} - 5w^{2} + 2w + 2]$ | $-e^{3} - 6e^{2} + 3e + 18$ |
| 59 | $[59, 59, -w^{4} + 2w^{3} + 5w^{2} - 5w - 4]$ | $\phantom{-}e^{3} + 8e^{2} + 9e - 28$ |
| 59 | $[59, 59, -w^{4} + 2w^{3} + 3w^{2} - 3w]$ | $\phantom{-}2$ |
| 79 | $[79, 79, 2w^{4} - 5w^{3} - 6w^{2} + 14w + 4]$ | $\phantom{-}\frac{5}{2}e^{3} + 18e^{2} + \frac{23}{2}e - 55$ |
| 79 | $[79, 79, -w^{4} + 3w^{3} + 3w^{2} - 9w - 5]$ | $-\frac{1}{2}e^{3} - 4e^{2} - \frac{7}{2}e + 11$ |
| 83 | $[83, 83, -2w^{4} + 5w^{3} + 8w^{2} - 16w - 10]$ | $-\frac{7}{2}e^{3} - 24e^{2} - \frac{21}{2}e + 67$ |
| 101 | $[101, 101, w^{4} - 3w^{3} - 4w^{2} + 11w + 4]$ | $-2e^{3} - 16e^{2} - 13e + 52$ |
| 103 | $[103, 103, -w^{4} + 2w^{3} + 5w^{2} - 5w - 6]$ | $-\frac{1}{2}e^{3} - 4e^{2} - \frac{3}{2}e + 13$ |
| 107 | $[107, 107, -2w^{4} + 4w^{3} + 8w^{2} - 10w - 7]$ | $-e^{3} - 8e^{2} - 7e + 32$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $2$ | $[2, 2, -w^{2} + 2w + 1]$ | $1$ |